Gas confining apparatus



Oct. l, 1963 Filed Jan. 15, 1958 OKI/fwd' A'C. z

.Source E. S. WEIBEL GAS CONFINING APPARATUS fana/*afar Sheets-Sheet l INV ENTOR.

0MM/'loam @v/4J@ Oct. 1, 1963 E. s. wl-:IBEL 3,105,803

GAS CONFINING APPARATUS Filed Jan. 15, 1958 2 Sheets-Sheet 2 F 7501 Maa/e United States Patent C) 3,105,803 GAS CUNFINNG APPARATUS Erich S. Weibel, Redondo Beach, Calif., assigner, by mesne assignments, to Space Technology Laboratories, Inc., El Segundo, Calif., acorporation of Delaware Filed Jan. 15, 1958, Ser. No. 709,122 3 Claims. (Ci. 20d-193.2)

This invention relates to a method and apparatus for confining gas within a predetermined volume and7 while not limited thereto, is herein described as embodied in a gas confining method and apparatus utilizing electromagnetic radiation.

In accordance with the invention the gas to be confined is first ionized to render at least a portion of the gas electrically conductive. The at least partially conductive gas is subjected to an electromagnetic field of a character such lthat the gas is compressed andheated. In one embodiment of the invention, gas within a resonant cavity is subjected to radio frequency electromagnetic radiation, the radiation first ionizing the gas and then supplying an electromagnetic radiation pressure between the ionized gas and the walls defining the cavity. The radiation pressure compresses the gas to a relatively small region within the cavity. Consequently, high temperature gaseous phenomena may be studied without the problems attendant on mechanical confinement of a compresesd, heated gas. Thus, for example, the radiation pressure may be used to confine the gas to a region within the cavity spaced apart from the cavity walls. In such a case the melting point of the material of the walls is not a direct factor on the upper limitation of the temperature of the gas to be confined.

According to another embodiment the radiation gas confinement arrangement described is supplemented with a magnetic gas confinement arrangement. In this embodiment the radiation gas connement arrangement is used to supplement and contain within la predetermined volume the unstable magnetic confinement arrangement so as to take advantage of the relatively low input power requirements of' the magnetic confinement arrangement.

According to a still further embodiment a radiation gas confinement arrangement according to the invention is used to provide a source of high velocity ions.

In the drawing, wherein like reference characters refer to like parts:

FIGUIRE i1 is a schematic representation of a gas confinement arrangement embodying the principle of the invention;

FIGURE 2 is la schematic illustration representative of gas confinement apparatus embodying the principle illustrated in FIGURE 1 as used in practicing one form of the invention;

FIGURE 3 is a sectional view taken along lines 3 3 of FIGURE 2; Y,

FIGURE 4 is a fragmentary sectionall view taken through line 4 4 of FIGURE 3;

FIGURE 5 is a graph illustrating an aspect of radiation confinement according to the invention;

FIGURE 6 is a graphical illustration of the intensities oft-he electric and magnetic fields in one mode of operation of gas confinement apparatus of the type illustrated in FIGURES 1 and 2;

FIGURE 7 is a graphical illustration of the intensities of the electric and magnetic fields in another mode of op-V eration of gas'coniinement apparatus of the type illustrated in FIGURES 1 and 2;

FIGURE 8 is a graphical representation of a confinement arrangement employing both radiation and magnetic energy for the control or" gas under conditions of high compression and high temperature; and

3,105,863 Patented 0er. 1, i963 FEiGURE 9 is a partially schematic representation of an ion source arrangement according to the invention.

The method and apparatus of the invention is based upon the known principle that reflected electromagnetic radiation exerts on the reflector a pressure commonly known as light or radiation pressure. While the magnitude of radiation pressure ordinarily experienced (for example, that experienced as radiation from the sun) is relatively low, the arrangement according to the invention provides a means for utilizing radiation pressure in a form wherein iappreciable 'force is exerted by this pressure. This utilization of radiation pressure is realized in one form of the invention by providing a resonant cavity in which radiation is allowed to be reflected between the walls defining the cavity and the gasto be confined. The magnitude of the radiation pressure is made large enough (by an appropriate radio frequency energy input) so that, when the gas is subjected tto Ithe radiation, it is first ionized and then comined to a relatively small volume within the cavity by the interaction of the ionized gas with the electric and magnetic fields of the confining radi-ation.

The Vprinciple of the invention will be described in con'- nection with FIGURE 1 where there is shown schematically a high temperature gas observation apparatus l. A toroidal container or toroid 2, made o-f conduc- I tive material and defining a resonant cavity therein, is

used asV a physical container within which the gas to be studied is compressed and heated. A window 3 is disposed in the walls or" the toroid 2 so that gas within the toroidal cavity may be observed. The window 3 has a conductive inner surface so as to avoid a gap in the cavity walls at the window.

For convenience of explanation the following dimensional notations will be used: the minor radius of the toroid will be referred to as b, the major radius of the toroid as A, the minor circumference as .s, and the radius of the toroid gas body within the toroid 2 as a (FIGURE 3). The actual dimensions may be, as will be described below in connection with an example of a gas body having a temperature of the order of 3x108 degrees Kelvin and an electron density of 1019 electrons per cubic meter, a=.16\8 centimeter, b=4.64 meters, and A=46.4 meters. f

As shown in FIGURE 1, a radio frequency oscillator 4 is connected to the toroid 2 to supply radio frequency energy to the cavity therewithin, a vacuum connection 8 is used to evacuate the toroid 2 to a vacuum of the order of about 106 millimeters of mercury, and a gas supply source 5 is connected to the toroid Z for supplying the toroidal cavity with the gas to be studied. 'This oscillator 4 may be any of the known radio frequency oscillators and may, for example, be Iany of the usual magnetron oscillators known in the art such as the one illustrated on page 163, Radar System Fundamentals, Navships 900,017, published by the Navy Department, Washington, D.C. The wave length of the radio frequency energy supplied by the oscillator 4 to the toroid Z is of the order lof twice the length of the minor radius b of the ytoroidwhen the toroid is excited Vin the TEM mode (the wave length being of the order of 6 centimeters for atoroid having a minor radius b of 3 centimeters), and t-he wave length is of the order of four times the length of the minor radius b when the toroid is excited in the TMm mode. The TE and TM modes of operation will be referred to in greater detail below.

At any given high temperature the kinetic energy of the gas gives rise to an output of a known spectrum of light or other extremely short wave length electromagnetic radiation. A photocell, spectroscopie, or similar detector 6 is connected for observation of the gas within the toroid 2. The detector 6, in turn, is coupled to the oscillator 4 to control, as desired, the frequency and/ or amplitude of the energy supplied by the oscillator to the toroid. Since oscillator frequency and amplitude control arrangements are well known in the art they will not be further discussed here. The magnitude of the electromagnetic energy supplied to the toroid is dependent upon the degree of gas compression and heating desired. The electromagnetic energy supplied by the oscillator 4 to the toroid 2 may be supplied either continuously or in pulses. In the latter case the pulsed operation of the oscillator may be realized by storing energy in a capacitor (as will be described in greater detail in connection with FIGURE 2) and periodically discharging the capacitor.

The mechanism of the operation of the gas control method and apparatus of the invention will now be discussed. In order to maintain the gas to be studied confined to the central region of the toroidal cavity, the space within the cavity is excited in either the transverse electric mode TEM or in the transverse magnetic mode TMm when the toroid 2 has a substantially circular small cross section. These modes give rise to the electric (E) and magnetic (B) field configurations illustrated in FIGURES 6 and 7 in which toroidal cavity radius is plotted against field strength. While, as will be described, both the transverse electric (TE) and the transverse magnetic (TM) modes may be used in providing the radiation pressure described, the TM mode is preferred. The reason for this is that the TM mode requires a smaller amount of confinement power than the TE mode to realize a given degree of gas confinement. The lower power requirement arises from the fact that in the TM Inode the magnitude of the magnetic field in the region of the surface of the gas body under confinement is inversely proportional to the radius a of the gas body. The relationship is actually constant a log a The particular electric (TE) or magnetic (TM) mode used is chosen such that the electric field (E) of the radio frequency energy has a voltage null or node confined to a central region of the cavity, that is, a node that does not extend to the cavity walls. Consequently, among the transverse electric modes, the use of electric mode TEM (FIGURE 6) is preferred in a toroidal cavity of the type shown in FIGURE l since this electric mode appears to be the only one in which the electric field (E) of the radio frequency energy has voltage nodes or nulls in only one effective region within the cavity, that is, along the region of the cavity adjacent to the center of the cavity. Actually, the electric field (E) in the TEM mode also has voltage nulls along the walls of the toroid but, as will be explained, these latter nulls are unimportant. As will be shown in connection with Equations 22 and 23 below, a charged particle (such, for example, as an electron or charged ion) is attracted to a node of an electric field. Therefore, ionized gases will be attracted to the center of the cavity and to the walls defining the cavity. Those gases that move to the central region of the cavity will be maintained there, while those gases that reach the walls will be neutralized on contact with the walls and will eventually drift toward the central region of the cavity Where, on becoming ionized, they will be trapped by the central voltage node. The magnetic field (B) in the TEM mode has substantially equal field intensities in the central and wall regions of the cavity and contributes to the attraction of ionized gases to the central and wall regions in a manner similar to that described with respect to the electric field (E).

Among the transverse magnetic modes the use of magnetic mode TMO, (FIGURE 7) is preferred in a toroidal cavity of the type shown in FIGURE 1 since this magnetic mode is apparently the only one in which the magnetic field strength in the central region of the cavity Bhf):

can be made substantially greater than the field strengths of the magnetic and electric fields in any other region of the cavity. In the TM01 mode, With a given gas density or gas body radius a and magnitude of electromagnetic gas confinement radiation, the ratio of the magnetic field strength at the cavity walls to the magnetic field strength at the surface of gas filament is, as indicated above, substantially inversely proportional to the ratio of the small radius b of the toroid to the small radius a of the gas filament.

While the toroid 2 illustrated by way of example has a circular small cross section it will be appreciated that the cross section may take different forms. For example, the small cross section may instead be elliptical or rectangular in form; in such a case TE and TM modes other than those mentioned above may instead be used provided no nodal surfaces extend to the cavity walls. For convenience of construction the force fields providing gas containment action have been described with reference to a toroidal resonant cavity. It will be appreciated, however, that other cavity contours may instead be used. For example, an elongated container may be used provided that means are used to prevent gas losses at the ends of the container. The ends of the container may be sealed by means of magnetic fields positioned at the ends of the cavity so as to, in effect, pinch off the ends of the cavity with magnetic fields. One such pinching arrangement will be described in connection with FIGURE 9.

Since a gas confinement arrangement of the type described requires an appreciable amount of power input, an auxiliary magnetic field may be used in combination with the radiation pressure arrangement described to provide a resultant confinement force which requires appreciably lower confinement input energy. The auxiliary magnetic field may, for example, be of the well known pinch effect type described, for example, in the article entitled Controlled Fusion Research-An Application of the Physics of High Temperature Plasmas, by Richard F. Post, on pages 345 and 346, in Reviews of Modern Physics, volume 28, number 3, July 1956, published by the American Institute of Physics, New York, N.Y.

The auxiliary magnetic field referred to may be realized by inducing an electric current in the gas within the toroid 2 once the gas has been rendered conductive by virtue of being ionized by the electromagnetic radiation supplied by the oscillator 4. A primary coil 7 is disposed closely adjacent to the toroid 2 and in a plane substantially normal to the major axis of the toroid. If the conductive walls defining the toroid 2 are constructed to be -substantially transparent to the field from the primary coil 7 (one such toroid construction will be described i-n connection with FIGURE 2), the primary coil will induce a current in the gas. This induced current gives rise to a magnetic field that provides the auxiliary magnetic gas confinement field referred to.

As will now be explained in connection with FIGURES 2 to 4, the novel method and apparatus of the invention may be used to ycontrol a thermonuclear of fusion reaction and has present research utility in that field.

As is known, if a hydrogen isotope, such for example as deuterium, is heated to a temperature of the order of tens or hundreds of millions of degrees Kelvin a thermonuclear reaction is produced wherein energy is released by means of what appears to be conversion of mass to energy. Some of the released energy appears to be in the form of kinetic energy of the reaction end products, that is, of neutrons and charged particles. Some of this kinetic energy is apparently transformed into what is commonly referred to as Ibremsstrahlung radiation, that is, exceedingly short wave length electromagnetic radiation such as hard X-ray radiation. A sustained output of bremsstrahlung radiation, requiring a sustained thermonuclear reaction, can be used to provide useful power in the form of electricity, the electricity being produced by an appropriate energy converter such as a-steam generator utilizing means for absorbing the bremsstrahlung radiation and converting it into heat. Some of the kinetic energy of the charged particles can apparently be converted directly into electricity by 'the interaction of the charged particles with applied electromagnetic fields, the electrical energy being produced by the motion of the moving particles through the electromagnetic iiux lines.

The thermonuclear reaction control means according to the invention will ybe described in connection with FIGURES 2 to 4. The gais to be subjected to the thermo nuclear reaction, for example a hydrogen isotope such as `deuterium or tritium, is first ionized as 'by being subjected to electromagnetic radiation. The ionized gas is then subjected to radiation pressure of a magnitude and character such that a stable, steady-state confinement of the gas body is realized, the gais body taking the form of a gas lament. A toroid 10, defining a resonant cavity therein, is used as a physical container with-in a central portion of which the thermonuclear reaction referred to is to be confined. The toroid 1t)y has a major radius A that is larger than its minor radius b (FIGURE 2). The minor radius b, in turn, is preferably appreciably larger than the radius a of the gas filament undergoing thermonuclear transformation. 2F01' example, the minor radius b may be of the order of about 100` to about 1,000 times larger than the gas filament radius a. In the interest of simplicity of illustration and explanation this ratio is not shown to scale in FIGURE 3. 'This ratio is desirable in order to insure that, as explained above in connection with the desired modes of operation, the iield strength of the confining radiation is appreciably larger at the surface of the gas filament than at the surface of the toroidal cavity. The resonant cavity within the toroid is defined by conductive Walls. The walls, for reasons to be explained in connection with FIGURE 8, are made up of a number =of conductive rings or bands 112 encircling the meridian or small circumference s of the toroid 10. Each of the conductive bands 12, which may for example be of a conductive material such as copper, are insulated from adjacent conductive bands by insulating material 14 iso that the toroid 10 -is effective fto conduct electric current substantially only in directions along the small circumferences s of the toroid, that is, along planes containing the large axis of the toroid.

A radio Ifrequency oscillator 24 is connected to the toroid 10 to supply radio frequency energy to the toroidal cavity therewithin. 'Ihis oscillator 24 is preferably of a high power type capable of `being tuned over a frequency range such that radio frequency energy may be fed into the toroid at a wave length anywhere from (for TMm mode operation) as large as 4b to one as small as a small fraction of b. The oscillator may be one of the conventional high power oscillator circuits such, ttor example,

as one which lends itself to the use of such high power output tubes as power tricde Radio Corporation of America type 5831.

A supply 26 lof the gas to be utilized Within the toroid 10, deuterium in the form of the yinvention here exemplified, is connected for entry into the toroid. While the use of deuteriurn may lbe preferred due to its relatively low cost at this time, a mixture of tritiumand deuterium may instead be used. In such case the required operating temperature of the thermonuclear reaction is reduced from the order of 100 million degrees Kelvin to the order of 10 million degrees Kelvin. However, the use of tritium, either alone or in combination with deuterium, is not presently preferred due to the high cost and radioactivity of tritium. While still other nuclear transformation reactions may be eiiected lby the use of the methodv and apparatus of the invention, such as fusion reactions involving the use of other substances having large reaction cross-sections such as lithium?, these other reactions are also not preferred at this time since deuterium is presently cheaper and easier to work with.

A `fusion thermonuclear reaction may be created and confined within the toroid 10 by means of the following: A desired quantity of deuterium gas from the gas supply 26 is fed into the toroid 10. The quantity of gas used is determined by the output desire-d, the power output being a function of the quantity of gas in the toroid. The gas introduced into the container may be at ambient temperature and at a relatively low density, that is, at a temperature of the order of 300 degrees Kelvin and a density of the order of l012 particles per cubic centime-ter. Radio frequency energy from the oscillator 24 is then fed into the toroidal cavity. This energy ionizes and heats the gas until the gas is substantially completely ionized, that is, to a temperature of the order of 100,000 degrees Kelvin. As the gas ionized and heated radiation pressure, from radio frequency energy reiiected from ionized gas and the walls of the cavity, exerts a force on the gas urging it in directions away from the walls forming the cavity land toward the center of the cavi-ty. The exertion of this Iforce on the ygas increases its temperature to of the order of a hundred million degrees Kelvin, corresponding torparticle velocities of the order of tens of thousands of miles per second, and increases its density to the order of l0M particles per cubic centimeter. The density of the gas in the toroid at this stage is illustrated in FIGURE 5 whe-re density d is plotted against radius a as measured along the minor radius of the toroid 10 (FIGURE 2). rIt will Ibe noted that the density of the gas is now highest at the center o of the toroidal cavity and -falls oft until substantilly no gas is present in regions adjacent to the walls defining the cavity. A thermonuclear reaction -now takes place in the center regions of the toroid wherein the deuterium nuclei 1H2 have enough kinetic energy to overcome their mutual electrostatic repulsion and are yconverted either directly or indirectly into at least helium nuclei (2He4), neutrons (n), and the hard radiation referred to as bremsstrahlung radiation.

If it considered that the main thermonuclear reaction involves the transformation of deuterium (1H2) into either light helium (2l-lea) and neutrons (n), or tritium (1I-I3) and ordinary hydrogen (lHl), the two reactions occurring with about equal probability:

2He3n+3.25mev. (million electron volts il o kinetic energy) ilU-l-iH2 Some of the tritium (1I-I3) thus formed will react with deuterium (11112):

and some of the light helium (2l-lei?) Will react with deuterium (1I-I2):

Thus, as 1an end product there is produced ordinary hydrogen (1I-I1), ordinary helium (2He4), neutrons (n), and

kinetic energy. It is this kinetic energy that produces the brernsstrahlung energy referred to. While ordinary hydrogen (1I-I1) may take part in lthe fusion process, the amount of energy produced by such fusion would be relatively small in comparison to the other fusion processes described above. For example, while la 1H2 plus 1H2 reaction may take .00003 second at the :fusion reaction temperat-ures referred to, a 1H1 plus ,H2 reaction takes of the order of one-half second (to produce 2H3 plus hard radiation Iplus 5 mev.).

As indicated in FIGURES 2, 3, and 4, means are provided for extracting energy Ifrom the fusion reaction described. Wa-ter is fed from an inlet pipe 27 (FIGURE 2) into coils 28 (FIGURE 4) within the Walls of the toroid 10 for absorbing the heat produce-d .by fbremsst-rahlung radiation from the fusion reaction. The coils 28 represent only schematically the energy absorption means lto be used for extracting energy from the fusion reaction. In practice, the coils 28 may instead tbe other energy absorption material. This bremsstrahlung radiation heats the water converting it into steam. The steam is then fed out of the toroid through an outlet pipe 29 and into a steam utilization device 31. The steam utilization device 31 may be any of the known devices of this type, such as a steam turbine, and will therefore not be further described. The steam utilization ydevice 31 is coupled to an electrical generator 33 for driving it to produce an electric output. A portion of the electric output may be used to provide the energy required for operating the radio frequency oscillator 24. To this end the electrical generator 33 may be connected to a capacitor 35 for storing a required amount of electrical energy, the stored energy being fed into the radio :frequency oscillator as required. Since electrical energy storage by means of capacitors is well known in the art such storage will not be described in further detail.

lf the compressed charge particles are periodically allowed to expand Within and against the electromagnetic field provided by the radio frequency oscillator 24, there is produced within the toroid an increased radio frequency field. At least part of the electrical energy from this field can be extracted from the toroid 10 by means of a wave guide output such as the wave guide used for feeding energy from the radio frequency oscillator into the toroid. Thus, some of the end product of the thermonuclear reaction may be extracted directly as electrical energy. Some of this electrical energy may be fed into a desired electrical utilization device through outlet 37 connected to the Wave guide 2S, and some of the energy may be fed back to the radio frequency oscillator 24 to serve as at least part of :the energizing source for it. Alternatively, as in the case of the electrical ener-gy output from the generator 33t, some of the electrical energy fed into the wave guide 25 from the toroid 10 may be stored in the capacitor for later use by the radio frequency oscillator. As has been indicated before, the Wave length of the radio 'frequency energy supplied by the radio frequency oscillator 24 to the toroid 10 is of the order of four times the length of the minor radius b (FIGURE 3) of the toroid 10 when the toroid is excited in the TM01 mode. The foregoing is the case substantially only when the gas within the toroid has not been heated and compressed to a sufficient temperature to cause it to act as la well defined filament -or inner conductor of a coaxial resonant cavity. After the `gas becomes sa conductive filament and thus a reflective gas body, the effective minor radius of the toroid becomes, instead, the distance between the outside surface of the gas body and the cavity walls. rIlhen, as indicated before in connection with FIGURE 7, it is desirable to have the peak field strength B of the magnetic field at a, the surface of the gas body. Thus, instead of the required Wave length being four time-s the length of the minor radius b, the actual Wave lengthV should be four times the distance between the gas body and the cavity walls. Furthermore, since lthe gas body radius a decreases vvith increasing electromagnetic radiation pressure and consequent increase in temperature, the wave length of the radio lfrequency energy should correspondingly increase during gas compression so that the four times ratio referred to is preserved. Consequently, the radio frequency oscillator 24 is preferably of la variable frequency variety so that the frequency changes referred to may be made. (In the case of the TEM mode no peak magnetic fields are involved; therefore, no corresponding decrease in frequency is required of the radio frequency oscillator 24.) An appropriate detector 39, which may be a detector of the kind referred to in connection wi-th the detector 6 of FIGURE 1, is used to sense the temperature of the gas body within the toroid lit and, since the radius of lthe gas body is a function of temperature, detect the radius of the gas body. This information is fed to an appropriate detector output device 41 which serves as means for controlling the frequency of the radio frequency oscillator. While 4the wave length of the radio frequency energy, in the TM mode excitation, is preferably made a function of the distance between the cavity walls and the gas body, in the event the frequency is not decreased with decreasing radius a as indicated above the transfer of energy from the radio frequency oscillator 24 to confinement energy within the toroid will still be effected though not as efficiently las when the :frequency is adjusted. Consequently, the use of a variable frequency radio frequency oscillator is preferred. As in the case of the detector 39 for the frequency control means of the radio frequency oscillator 24, another detector 45' may be connected to the toroid 10 for determining when an additional supply of deuterium is required. To this end the deuteriurn supply detector 45 is connected to the control valve 23 of the deuterium supply 26 so las to feed a required charge of deuterium into the tor-oid 10 When required.

As indicated before, an auxiliary magnetic field may be used in combination with the radiation pressure arrangement described to provide a resultant confinement force that requires an appreciably lower confinement input energy. Referring to FIGURE 2, the supplemental magnetic pinch field is provided by low frequency electric energy, for example 60 cycle alternating current, which is fed from an appropriate energy source into the resonant cavity in the toroid 10 by means of a transformer 16. The transformer 16 is coupled to the toroid l0V for inducing a secondary current in the ionized gas to be contained within the toroid. The transformer 16 has a transformer core 20 linked to the toroid 10i (the core being any conventional transformer core material such as laminated sheets of silicon steel) and a primary winding 22 Wound around the core 20. Therefore, the electric fields induced by the primary winding 22 lie in planes normal to the major axis of the toroid. Since, as has been indicated above, the conductive bands 12 that define the resonant cavity of the toroid do not extend any appreciable distance along the major circumference of the toroid, the body of the toroid is substantially transparent to energy induced by the primary winding; only conductve gas 13 within the toroid will be able to receive induced energy from the transformer. Also, in the case where the transformer 16 is used to provide the supplemental magnetic gas confinement field, the energy extraction coils 28 (FIGURES 3 and 4) or their equivalent, described above, are made either of an electrically nonconductive material or of short sections of conductive material in order to insure against a shunting of the transformer fields by the coils.

If the gas 1S has been previously subjected to suf`n`cient radiation from the radio frequency oscillator 24 to become substantially completely ionized, say at a temperature of the order of about one hundred thousand degrees Kelvin, the ionized gas becomes sufficiently conductive to act as a filament of plasma forming a toroidal transformer secondary Winding running substantially along the center line of the toroidal cavity. The energy from the transformer is thus fed directly to the lilamentary plasma giving rise to the substantially magnetostatic pinch effect referred to. The magnetostatic pinch may be made of sufficient magnitude to provide the greater portion of the power input required to establish the desired confinement of the gas. The radiation pressure supplied by the oscillator 24 is made only of as large a magnitude as required to force back toward the center of the toroidal cavity any gas which would otherwise tend to escape from the center by virtue of the known kinks or instabilities (described on page 347 of the article referred to) inherent in magnetic pinch confinement. Thus, the magnetic pinch confinement provides the greater portion of the required confinement energy, and the radiation pressure fields render stable the magnetic confinement by forcing back to the center of the toroid any gas which might tend to momentarily escape the magnetic confinement force and flow toward the walls of the toroid.

When the combined radiation pressure `and magnetost-atic gas confinement arrangement is used the gas is packed closer to the center of the toroid (as indicated in FIGURE 8) than when radiation confinement alone is used (the latter being represented in FIGURE In the case of the combined fields confinement the density of the gas at the center of the toroid is of the order of 1017 particles per cubic centimeter at temperatures of the order of l()8 degrees Kelvin. A thermonuclear reactor according to the -combined arrangement may, `for example, have a power output on the order of 1014 watts if radius b`=10 meters, radius a=.3 centimeter, and the thermonuclear -gas temperature is about 1..2. 109 degrees Kelvin.

As indicated above with respect to the reaction teniperature detectors 39 and 45, a further detector 21 may be connected to the toroid 10 for determining the required Iamplitude of current required to provide the desired supplemental magnetic field. The output from the detector 21 is connected to current control apparatus 49 for controlling the magnitude of current through the transformer primary 22 as a function of the temperature of the gas within the toroid 10. Similarly, the detector 21 may also be connected to the radio frequency oscillator 24 for controlling the magnitude of radiation pressure energy supplied tothe toroid 10.

While a gas confinement arrangement has been described with respect to a method and apparatus for providing an opportunity to observe high temperature gases, it is realized that the confinement achieved in the manner herein described may be used for other end purposes. For example, as illustrated in FIGURE 6` the linear confinement arrangement referred to may be used to provide a Asource of high Velocity charged ions. An elongated container 30, having a closed end portion 32 and an aper- -tured opposite end portion 34, defines a resonant cavity or chamber therein. A controlled amount of gas from a gas source 46 is heated to a desired temperature and then allowed to escape through the aperture 36 in the` apertured end portion 34 to provide a high velocity stream of charged ions.

As in the case of the tonoidal gas confinement arrangement described with respect to FIGURE 1, the container 30 is made of a conductive material. While magnetic elds, provided by electromagnets 38 and 401, are used to prevent heated gas within the container from reaching the ends of the container, these fields react magnetically with the gas within the cavity and penetrate conductive material such as copper. Thus, the single cylindrical conductor does not impede the action of these magnetic fields. One of the electromagnets 40 is adapted to be connected to a variable voltage source, as indicated by the variable connection to the battery 42, while the other of the electromagnets 38` is connected to a `single voltage source. The variable voltage source afforded one of the electromagnets 40 allows the magnetic field of that electromagnet to be diminished to an extent sufficient to allow ions 43 to escape from the container 30 and through the aperture 36 in one of the end walls 34 of the container.

As in the case of the toroidal arrangement of FIGURE 1, -a radio frequency oscillator 44 is coupled to the cavity defined by the elongated container 30 to provide the required electromagnetic radiation pressure lield. This radiation pressure field preserves the side walls of the container from the gas and heats the gas to a desired ternperature, while the magnetic fields from'the electromagnets 3S and 40 control their spacing of the gas from the end walls 32 and 34 of the container.

As has been indicated above, a certain amount of energy will be lost from the radio frequency electromagnetic radiation pressure field in the cavity to the walls defining the cavity, the loss being the consequence of waves penetrating the walls. .This radio frequency energy loss must be made up by increased energy input from the radio frequency energy source. Since the losses in the walls of the conductor are 'resistance losses, they can be substantially eliminated if the walls are made superconductive, that is, if the walls are cooled by well-known liquid hydrogen or liquid helium cooling apparatus (not shown) to a temperature close enough to absolute zero so that the well-known phenomenon of superconductivity is effected. Since the temperature required for superconductivity is lower in the presence of high intensity magnetic fields than in the absence of such fields, the temperature of the cavity walls must be maintained closer to 0 K. than in the more usual superconductive arrangements where no magnetic fields are present.

That the electromagnetic radiation field referred to can effect the required conning action can be seen from the following analysis. The analysis will be made in connection with the TMOI mode excitation referred to.

Consider a cylindrical cavity of radius b, of infinite length, and defined by a perfectly conducting wall. Let the axis of the cavity coincide with the axis of a cylindrical coordinate system r (radial distance), g' (azimuth distance) and z (axial distance). A complete description of the plasma and the confining field is afforded if the following quantities are known as functions of space and time:

The number density of electrons n The number density of ions N The electric field E .a The magnetic field B The electromagnetic field is subject to MaxWells equations where p represents the charge density, t represents time, and j' represents the combined current of electrons and ions. The charge density and the current density are related to the number densities by the following equa-V tions:

or ion, and where V and v are the velocities of the ions and electrons, respectively.

The gas or plasma to be confined will thus be treated as a mixture of t-wo gases which are oppositely charged. The forces acting on these gases are:

a F=Ne[El-{VXB] and f=-ne[E{-vXB] (7) Y F and f representing, respectively, the forces acting on the ions and the forces acting on the electrons. It will be assumed that both gases are at the same temperature so that their partial pressures are P=NkT and p=nkT (8) respectively, k being Boltzmanns constant, T representing temperature, and P and p representing,respectively, the partial pressure of ions and electrons. The motion of the gases is governed by Newtons law for change of momentum:

where M and m represent, respectively, the masses of 11 an ion and electron, and t represents time. Finally the continuity equations for both ions and electrons must be This description of the plasma is essentially macroscopic. The effect of collisions between like particles is summed up in their partial pressures. Collisions between unlike particles are neglected. The coulomb interaction is represented by Equation 5, which gives rise to an electric field, Equation 1, which in turn exerts forces on the particles, the irst terms of Equation 7. While the system of Equations 1 to l0 is relatively complex, it admits of a relatively simple solution.

To find this solution it is required that all quantities be independent of p and z and that only E, B, V, and v depend on t. E is written in the form:

E={Er(r)\, 0, E(r) cos (wt)} (ll) In this notation, the three terms in the bracket represent the r, g', and z components, respectively. -Finally it is required that the velocities have only z components:

It will now be shown how the system of equations breaks up into manageable portions. The continuity Equations 10 are already satisfied. From Equation 11 one iinds B using Equation 4:

={o, E/(r) sin wt, (13) where E' represents the derivative of E with respect to r. Dilerentiating Equation 2 with respect to t, and substituting Equations l1 and 13 into Equation 2, one obtains @Q 2 l i f l This Equation 14 expresses the currents `as the sources of the fields. Now we shall express them as caused by the fields.

Consider the momentum Equations 9. Neither the magnetic force nor the pressure gradient have components in the z direction. Hence the z components yof Equation 9 become V eNE @0S @Pariah-Wvg?) and -en cos wt=mn vgv) (15) The ion and electron velocities depend only on r land t, so one finds Diferentiating Equation 6 with respect to t, and using Equation 16, one obtains an nf n) t-(M-l-m Eeoswt The elimination of TUEnN-me (zo) Integrati-on ot Equation 16 yields ion and electron velocities V and v:

eE V-Mw cos wt and v= -e-E- cos wt (21) mw Now the cross products with B can be formed to obtain the magnetic par-t of the Lorentz force Equation 7. For the ions, one obtains -s 2 eNV B= g,{E-lf 5h12 at, o, o} An analogous expression is obtained for the electrons. The magnetic force thus has Ionly a radial component. The magnetic force is proportional to E2, and thus iS independent of the sign ot the charge! Thus ions and electrons experience a `force in the same direction! Also, while the magnetic force osoillates with a frequency Zw, it does not change sign with time since sin2 wt is always positive. This magnetic torce can `also be written Las @2N i 2 Fm'r- 4M2 dr(E (1-))(1 eos Zwt) (23) from which it can be seen that the magnetic force always points in the direction of decreasing E2, that is to the nulls lor nodes of E. Thus, as has been indicated 1before in connection with the discussion of the TEM mode a charged partie-le is 'always attracted to a node of an electric field. Since an electrical null or node will appear in the region of greatest ionized gas or plasma dens-ity, and the electrical field will increase in the direaction `of decreasing plasma density (because the latter has a low impedance), charged particles that 4.become separated from lthe main body of the plasma will be driven back into it.

The oscillating character of the magnetic force has a large effect only where the plasma frequency equals nearly 2w; this happens only in a small and unimportant region. Consequently, the oscillating part of this force may be disregarded. Thus, Equations 21, which are the radial parts of Equation 9, now become The problem is thus reduced to one of finding the solutions for the four Kordinary diiferential Equations 18, 20, 24, and 25, and for the four unknowns E(r), E,.(r), N(r), (r). To single out fthe particular solution of in- 'I he first of these conditions excludes solutions which are lsingular at r=0, the second condition specifies the intensity of the radiation field, and the third condition is 13 required by the presence of the perfectly conducting cavity wall. If N and `n are considered given, then Equation 18, together With the boundary condition Equations 26, 27, and 28, would characterize a Sturm-'Liouville i eigen-value problem, w being the-eigen-value. For the electrostatic iield one has, by symmetry,

Erf() =0 (29) In addition en@ should give the values of Nw) and 11(0) to completely determine the solutions. It appears, however, that this tis not possible. Therefore, one has to instead prescribe the total number of charges of each kind:

b b 21t- 0 Nrdr and 21.11;) mdr (30) lit will be assumed that the total charge in the plasma is zero, so that b .fom-manto (31) Thus one finds that E,(b) :v0 (32) On differentiation, there is realized dN M E1T5-0,T0,7`b

now be obtained for fthe limit of infinite coulomb interaction lin Equations 24 land 25 In this case no charge separation can occur and the problem is greatly simplied. The results thus obtained are representative of the nadiation 'confinement since the Coulomb interaction is very strong.

Starting from Equation 34, which does not contain the (innite) coulomb interaction, it is required that N--n (35) Thereore,

-eEZ t i N-n-n0exp- [SLMCT "L4-MY] (36) This Expression 36 is substituted in Equation 18 so that it becomes an ordinary second order diiierentiial equation Vfor EU):

. 37) E(r) vanishes. Equation 37 can be brought into la more convenient dimension-less form. Using thetcllowing transforma-tions: v

x=wrV i l azi/720) l 1 2(1) saar (WFM) and 'nge2 wz 14 one obtains u-+uf+ 1aeu2 u=o (a9) with the boundary conditions 11(0):U0, 14"(0) :0, and MUM) =0 (40) The fields and densities in terms of the function u(x) are EU) u emr 41) u BU) Va The solution u(x) depends on two parameters a and uo. The parameter is a measure lof the transparency of the plasma to the radiation, since the depth of penetration of an electromagnetic eld is given by d=l/w\/a-1. The cases of practical interest are obtained by choosing u Vand uo each appreciably less than 1. When a is appreciably less than 1 the plasma is dense enough to be a good reflector; when uo is appreciably less than 1 only a small amount of the radiation penetrates to the core of the plasma, and therefore determines the radius of the plasma column.

With these parameter values it is not diicult to perceive the general shape of the solution (x): For small values of x, u itself is small and er2 is equal to about unity, so that the differential equation has Ithe solution and of VWX) have a maximum at x, which defines a :radius 211 a= Ld It will be called the plasma radius because most of the plasma lies inside the cylinder with radius a. Thus the plasma is really confined.

`Ilf the solution u1(x) is continued beyond x2 where its lirst maximum occurs, the plasma density, e*u2 increases again. In a practical arrangement, however, one wants 'the density to be 4large only at the center x=0. Beyond x2 the particle density should stay small. i

To achieve this, assume that the plasma has been removed at points x x2. Mathematically this means setting a=0 in Equation 39 for x x2. The `discontinuity thus introduced in the higher derivatives of u is extremely small since, tat x2 :the term ae*u2=ae2 max is practically zeno. Thus the solution u continues after x2 as an `ordinary cylinder 'function laccording to Equation 43. The rst zerlc of u, namely x3=wb marks the radius of the cavity wa Y Physically, this removal of plasma upsets the equilibrium at x2 where the particle density drops from eu2 to zero. Consequently, particles will escape at a rate given by their density at x2, and 4by their thermal velocity:

The total number of particles confined is approximately 1ra2n(0). Thus the half life of the confinement is about a 2 x t 2Tzeu 2) At T=108 degrees Kelvin .this time ranges from 10300 to 10400 seconds. Hence, practically no leakage of plasma occurs.

Finally, let us examine u' (x) which represents the magnetic field B according to Equation 4l. At x1 (radius a in FIGURE l) u' has a sharp maximum. Outside this point it behaves very nearly like the magnetic field in a coaxial line, while inside it drops rapidly to zero (at radius in FIGURE 7) in a manner familiar from the skin effect in wires. It is important to note that the magnetic B field, and hence the magnetic pressure, 4is much larger at the plasma (r=a) than at the cavity wall (r=b). This effect is due to the cylindrical geometry and apparently occurs only for the TM mode with no qb variation. Equation 39 has been integrated numerically for various values of a and uo. As explained above, a is set equal to zero for x x2, where x2 is the first maximum of u.

In the chart below the values of or, un, x1, u(x1), x2, u(x2),.x3, and u(x3) are given for a number of different choices of the following parameters:

The plasma radius a=o The cavity radius b=3 The magnetic field:

l At the plasma mummy-$0 At the Wan B01) :./mwml Each pair of a and uo values .gives rise to a whole family of physical relationships since one is still free to choose a temperature T and a maximum density no.

o: un I1 u (I1) I2 11,(12) 17a u' (Is) .707 .027 43. 7 .704 6. 14 2. 70 -3. 89 .1 .04s 72.1 .sas 11.0 2. s2 7.17 10-2 .074 s0. 9 .954 15. 3 2. S8 10. 2 10-3 100 sa s 1. 026 1s. s 2. 95 12. 0 10-4 12s se. s 1. 09s 21. s 2. 97 14. s 10-25 14s a9. 5 1. 15 24. 5 3. 02 -10 7 707 0027 437 616 7. es 2. s 5. 40 .1 .0048 721 -a .0100 852 8134 30. o 2 76 19. 4 10-4 .0124 87s 8158 as. 5 2 7e -24. s 10-5 .0148 S95 .81s 40.1 2 76 29.7 10-5 0014s 8. 950

As for example, let us choose:

Ratio of plasma frequency2/ applied electromagnetic frequency2 a=l00, u0=103. Temperature T=3 10a degrees Kelvin. Electron density n=l019 electrons per cubic meter.

Thus: Applied electromagetic frequency 2.84X1l08 cyles per second. Plasma radius a=.00l68 meter. Cavity radius b=4.64 meters. Toroid radius A=46.4 meters. Mode TMm. Magnetic field strength at the surface of the plasma B(a)=.548 volt seconds per square meter. Magnetic field strength at the wall B(b)=-1.25 l02 volt -seconds per square meter. Maximum electric field strength Emax=5-8 X100 volts per meter nmm/nmx=l0390. Gas cominement time t=l()3"I8 seconds.

From the foregoing it is seen that electromagnetic radiation pressure may be used to confine an ionized gas to a relatively small volume even though the gas may be at extremely high temperatures.

While the arrangement of the invention has been described With respect to apparatus useful in the study of high temperature gases and in the provision of a source of high velocity charged ions, it will be appreciated that the arrangement may be used in other fields Where high gas temperatures or velocities are useful.

What is claimed is:

l. Gas confining apparatus including the combination of a container having electrically conductive walls deiining a toroidal chamber, said walls being reflective with respect to electromagnetic radiation of microwave frequency, a gas source connected to ,said container to introduce gas therein, and a source of microwave electromagnetic energy coupled to the container, said source of electromagnetic radiation having a selected frequency which establishes standing waves within the toroidal chamber in a configuration in which electric eld nodes are centrally disposed within the toroidal chamber for the confinementl of: gas therein spaced apart from the chamber walls, and a primary transformer winding positioned adjacent the toroidal chamber for producing magnetic fields which cooperate with the electromagnetic radiation within the toroidal chamber to confine the gas to an axial region of the toroidal chamber corresponding to the location of said electric field nodes.

2. Gas confining apparatus including the combination of a resonant toroidal chamber, a gas supply source coupled to the chamber, and a source of microwave energy coupled to the toroidal chamber having a frequency characteristic selected to produce a configuration of electric and electromagnetic fields within the toroidal chamber having an electric field node centrally disposed along an axis within the toroidal chamber so as to confine gas particles Within the chamber in a ring out of contact with the chamber, and a primary transformer winding positioned adjacent the toroidal chamber for producing a magnetic field within the chamber to cooperate with the electromagnetic field for the confinement of gas therein spaced apart from the chamber walls.

3. A plasma confining apparatus comprising a resonant toroidal chamber, an oscillator coupled to said chamber for establishing radio frequency fields having centrally disposed electric field nodes to confine the plasma to an axial region of the chamber, control means coupled between said chamber and said oscillator means responsive to temperature variations of plasma confined Within the chamber and adapted to correspondingly vary the frequency of the oscillator in such a manner that electric field nodes within the chamber are maintained in a position in the central region of said chamber, and means producing a magnetic field within the chamber to cooperate with the radio frequency fields in confining the plasma therein.

(References on following page) 1 7 References Cited in the file of this patent UNITED STATES PATENTS Nucleonics, February 1956, pp. 42-44.

Journal .of Applied Physics, May 1957, vol. 28 No. 5, pp. 519-521.

Journal of Nuclear Energy II, vol. 5 pp, 71-73, 84, 85, Pergamon Press, London.

TID-7536 (Pt. 1), Controlled Thermonuclear Reac- 18 tions, September 1957, publ. by A.E.C. Technical Information Service, Oak Ridge, Tenn., pp. 5-9, 26.

Physical Review, vol. 107, No. 2, Jul-y 15, 1957, pp. 345-350.

Nucleonics, August 1957, pp. 50-55.

Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, vol. 32, held in Geneva Sept. 13, 1958, United Nations, Geneva, 1958, pages 161-163.

Vol. 31 of the above, pages 292-297, 6, 20, 32, 38.

Knox: Australian J. of Physics, vol. 10, No. 1, March 1957, pp. 2,21-225.

Controlled Thermonuclear Reactions by Samuel Glasstone, D. Van Nostrand Co., N.Y., 1960, pages 437-445.

Journal of Electronics and Control, volume 5, July- December 1958, pages 435-438 (by Weibel).

UNITED STATES PATENT oFFIcE CERTIFICATE OF CORRECTION Patent Nml 3 IOSQBOS October l 1963 Erich S. Weibel It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column lines 43 to 46, the upper portion of the formula should appear as shown below instead of as in the patent:

2He3+n+325 meV(l (million electron volts 7 of kinetic energy) Column Il, line 2O9 strike out the arrow first occurrence; column l5u line l2c for "FIGURE l" read FIGURE Signed and sealed this 12th day of May l94 (SEAL) Attest:

ERNEST W.. SWIDER EDWARD L BRENNER Attesting Officer Commissioner of Patents 

1. GAS CONFINING APPARATUS INCLUDING THE COMBINATION OF A CONTAINER HAVING ELECTRICALLY CONDUCTIVE WALLS DEFINING A TORODIAL CHAMBER, SAID WALLS BEING REFFLECTIVE WITH RESPECT TO ELECTROMAGNETIC RADIATION OF MICROWAVE FREQUENCY, A GAS SOURCE CONNECTED TO SAID CONTAINER TO INTRODUCE GAS THEREIN, AND A SOURCE OF MICROWAVE ELECTROMAGNETIC ENERGY COUPLED TO THE CONTAINER, SAID SOURCE OF ELECTROMAGNETIC RADIATION HAVING A SELECTED FREQUENCY WHICH ESTABLISHES STANDING WAVES WITHIN THE TOROIDAL CHAMBER IN A CONFIGURATION IN WHICH ELCTRIC FIELD NODES ARE CENTRALLY DISPOSED WITHIN THE TORORIDAL CHAMER FOR THE CONFINEEMENT OF GAS THEREIN SPACED APART FROM THE CHAMBER WALLS, AND A PRIMARY TRANSFORMER WINDING POSITIONED ADJACENT THE TOROIDAL CHAMBER FOR PRODUCING MAGNETIC FIELDS WHICH COOPERATE WITH THE ELECTROMAGNETIC RADIATION WITHIN THE TORIDAL CHAMBER TO CONFINE THE GAS TO AN AXIAL REGION OF THE TOROIDAL CHAMBER CORRESPONDING TO THE LOCATION OF SAID ELCTRIC FIELD NODES. 